Brewer, Lewis & Goodman (2026) argue the reference class problem dissolves once likelihoods use proportions instead of population counts

anthropic-reasoningreference-class-problembayesian-inferencenick-bostromfull-indexical-conditioning

Brewer, Lewis & Goodman (2026) argue the reference class problem in anthropic reasoning — Bostrom's (2002) observation that different choices of which group of observers a reasoner is "randomly sampled from" appear to license different conclusions from the same evidence — is largely an artifact of how likelihoods are written down, not a substantive indeterminacy. Their worked example holds the reasoner's evidence fixed — a hypothetical Alice born in Wales — and varies only the reference class she is treated as having been selected from: first the union of Wales and the USA, then the larger union of the United Kingdom and North America. The two likelihoods differ only in their denominator, which is exactly why the choice appears to matter; the posterior conclusions of interest turn out to be unchanged, provided the class is large enough to contain the question being asked. In their words: "We ultimately conclude that reference class choices do not affect substantive conclusions, provided the reference class is large enough for the question being asked."

Their diagnosis is that the apparent dependence comes from writing likelihoods in terms of raw population counts rather than proportions; a coordinate change via the chain-product rule of probability removes it — "We conclude that the reference class problem is only an apparent problem caused by using population sizes in the coordinate system." The resolution is offered as a general feature of the Full Indexical Conditioning framework they develop (a framework Radford Neal named and discarded in 2006 — see companion claim), not a special case limited to the Wales example.

The paper is explicit about how far it has carried the argument: "In this paper we present intuitive arguments for this conclusion, leaving a more formal development of the theory of reference classes to a future contribution." The dissolution is therefore offered as a demonstration, not a theorem.

This is a striking claim to dissolve a named, decades-old foundational puzzle, from a single preprint not yet peer-reviewed; see question-corroborate-brewer-lewis-goodman-2026-fic-preprint for the vault's open corroboration tracking on this source.